Cloud computing extends Transportation Cyber-Physical Systems (T-CPS) with provision of enhanced computing and storage capability via offloading computing tasks to remote cloud servers. However, cloud computing cannot fulfill the requirements such as low latency and context awareness in T-CPS. The appearance of Mobile Edge Computing (MEC) can overcome the limitations of cloud computing via offloading the computing tasks at edge servers in approximation to users consequently reducing the latency and improving the context awareness. Although MEC has the potential in improving T-CPS, it is incapable of processing computational-intensive tasks such as deep learning algorithms due to the intrinsic storage and computing-capability constraints. Therefore, we design and develop a lightweight deep learning model to support MEC applications in T-CPS. In particular, we put forth a stacked convolutional neural network (CNN) consisting of factorization convolutional layers alternating with compression layers (namely lightweight CNN-FC). Extensive experimental results show that our proposed lightweight CNN-FC can greatly decrease the number of unnecessary parameters thereby reducing the model size while maintaining the high accuracy in contrast to conventional CNN models. In addition, we also evaluate the performance of our proposed model via conducting experiments at a realistic MEC platform. Specifically, experimental results at this MEC platform show that our model can maintain the high accuracy while preserving the portable model size.